The glitch as stated, no 300 black out spent case extractor,
As for the 7.62 broken case extractor, although the tip is right for the one Brownells sells, the back side is wrong to mate up with the bolt face.
Again, 30 cal brush is used for 223 and 300 black out cases, and 45 cal brush for 308 cases (ID of the main section of the case will determine the needed brush, since you want the bristles to be angled back just a few degrees). If the brass brush did not work, then get a New 30cal SS brush instead.
And pull the brush back to bend the bristles towards the back of the receiver inside the broken case without twisting the cleaning rod to the start of the neck of the case, and give the cleaning handle a hard single blow back down the muzzle so the bristles will bit into the inside of the case to drive the broken spent case out the back side of the receiver with the brush on the single piece cleaning rod tip.
Note, in a 223 case, you can just pull all the way back to the neck section, since the smaller neck of the 223 will not allow the brush to be pulled any farther forward towards the muzzle.